Before you send any kind of letters it's probably better to get a professional assessment and evaluate the correct procedure. You might, for example, implicitly confirm the existence of a rental contract if you sent a cancel notice. I'm not saying this would be the case, but better safe than sorry.

Your landlord is highly likely to be a member of the Swiss homeowner's association ("HausEigentümerVerband", SHEV). Ask LL for their member number and call the SHEV for professional advice, a first assessment may be free, but even if not they're people who specialise in that field.

Alternatively you could use Zürich City administration's free legal advice. See here. (15mins max, by appointment only, by personal appearance only)